Question: Given $ m \angle MON = 7x + 64$, and $ m \angle LOM = 7x + 18$, find $m\angle MON$. $O$ $L$ $N$ $M$
Explanation: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {7x + 18} + {7x + 64} = {180}$ Combine like terms: $ 14x + 82 = 180$ Subtract $82$ from both sides: $ 14x = 98$ Divide both sides by $14$ to find $x$ $ x = 7$ Substitute $7$ for $x$ in the expression that was given for $m\angle MON$ $ m\angle MON = 7({7}) + 64$ Simplify: $ {m\angle MON = 49 + 64}$ So ${m\angle MON = 113}$.